結果

問題 No.3145 Astral Parentheses Sequence
ユーザー 👑 hos.lyric
提出日時 2025-05-16 22:05:09
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 4,030 bytes
コンパイル時間 3,260 ms
コンパイル使用メモリ 137,472 KB
実行使用メモリ 6,272 KB
最終ジャッジ日時 2025-05-16 22:05:20
合計ジャッジ時間 4,664 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 45
権限があれば一括ダウンロードができます

ソースコード

diff # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }

string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }

struct ModInt {
  static int M;
  import std.conv : to;
  uint x;
  this(ModInt a) { x = a.x; }
  this(uint x_) { x = x_ % M; }
  this(ulong x_) { x = cast(uint)(x_ % M); }
  this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
  this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
  ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op, T)(T a) {
    static if (is(T == ModInt)) {
      static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
      else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
      else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
      else static if (op == "/") { this *= a.inv(); }
      else static assert(false);
      return this;
    } else static if (op == "^^") {
      if (a < 0) return this = inv()^^(-a);
      ModInt b = this, c = 1U;
      for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
      return this = c;
    } else {
      return mixin("this " ~ op ~ "= ModInt(a)");
    }
  }
  ModInt inv() const {
    uint a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
    assert(a == 1); return ModInt(y);
  }
  ModInt opUnary(string op)() const {
    static if (op == "+") { return this; }
    else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
    else static assert(false);
  }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  bool opCast(T: bool)() const { return (x != 0U); }
  string toString() const { return x.to!string; }
}

alias Mint = ModInt;


void main() {
  try {
    for (; ; ) {
      int N = readInt;
      const M = readInt;
      Mint.M = M;
      
      if (N % 3 != 0) {
        writeln(0);
        continue;
      }
      N /= 3;
      
      const L = 3*N + 1;
      auto lpf = new int[L];
      foreach (p; 2 .. L) lpf[p] = p;
      foreach (p; 2 .. L) if (lpf[p] == p) {
        for (int n = p; n < L; n += p) chmin(lpf[n], p);
      }
      
      auto es = new int[L];
      void add(int n, int val) {
        for (; n > 1; ) {
          const p = lpf[n];
          es[p] += val;
          n /= p;
        }
      }
      
      // binom(3n,n) / (2n+1)
      foreach (i; 1 .. 3*N + 1) add(i, +1);
      foreach (i; 1 .. N + 1) add(i, -1);
      foreach (i; 1 .. 2*N + 1) add(i, -1);
      add(2*N + 1, -1);
      debug writeln("es = ", es);
      
      Mint ans = 1;
      foreach (p; 2 .. L) ans *= Mint(p)^^es[p];
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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